The three were produced before the court of Judge S M Chandgade at suburban Bandra amid tight security with just two days left for the 14-day deadline for police custody to end.
After the court proceedings, they were taken back to Khar police station for further interrogation.
Seeking extension of custody, Special Public Prosecutor Vaibhav Bagade said "the accused (Indrani) remained uncooperative".
"Scope of probe is large. Accused is a hard nut to crack. They have used modern tools like email and Internet to plan the murder. Progress shown is already on record. We have not wasted a single day. They impersonated the victim by creating false email. She (Indrani) created bogus email id. Custody is short considering the vastness of investigation," Bagade said.
He said investigations were underway to ascertain who else helped Indrani and police needed reasonable time for its probe.
"We need to know who else helped her. Emails need to be studied. Crime was committed across jurisdictions. Bank accounts maintained by accused no 2 (Indrani) and accused no 3 (Sanjeev Khanna) are across UK and Mumbai. We need to investigate payments made from these accounts.
"We need to recover accused (Indrani's) credit card. Accused shows complete reluctance to cooperate. Additional offence under section 307 (attempt to murder) was added. The material and person with whom accused no 2 had contact need to be investigated. Police need reasonable time," Bagade said.
Rejecting the prosecution's contentions, the defence said Indrani is not a hardened criminal and accused the police of "conducting a media trial and prejudicing the proceedings".
"There is no medical evidence. Two days of police custody is a humiliation of my client. Accounts cannot be recovered from my client. She is in custody. They have to recover it from bankers," he said.
Indrani, her former husband Sanjeev Khanna and her former driver Shyamvar Rai have been arrested on the charge of murdering Sheena and disposing of the body in a Raigad forest in April 2012.
Police had last week exhumed remains of the body from Raigad forest and later claimed that digital superimposition of the profile of Sheena had matched with the skull recovered from the forest.
The remand application of police stated that the planning to kill Sheena's brother Mikhail started from Kolkata. Mikhail has alleged that Indrani had tried to kill him too.
Police had also interrogated Indrani's husband and media baron Peter Mukerjea for three days, though he is not an accused in the case.
Mikhail had flown in to Mumbai last week from Guwahati. He was also questioned by police.
Others who were questioned in connection with the case included Peter's son Rahul Mukerjea and Vidhie, daughter of Indrani and Sanjeev Khanna.
Police have also questioned Siddharth Das, biological father of Sheena and Mikhail.
Sheena was engaged to Rahul, Peter Mukerjea's son from an earlier marriage, when she was allegedly murdered on April 24, 2012.
The 24-year-old was allegedly strangled in a car, then her body was burnt and dumped at a forest in Raigad, about 84 km from Mumbai.
Why we are so keen on demonising Indrani
The Sheena Bora case and the ugly face of Indian news
Rahul Mukerjea got 6 messages from 'Sheena' after disappearance
The cop who cracked the Sheena Bora case
Sheena Bora case: 'Follow the money trail'